|
%I #19 Mar 24 2020 14:04:43
%S 1,2,3,3,5,6,7,5,7,10,11,9,13,14,15,9,17,14,19,15,21,22,23,15,21,26,
%T 19,21,5,30,31,17,33,34,35,21,37,38,39,25,41,42,7,33,35,46,47,27,7,42,
%U 51,39,53,38,55,35,57,10,59,45,61,62,49,33,65,66,67,51,69,70,11,35,73,74
%N Number of distinct 7th powers modulo n.
%C Compare with enigmatic similarity of analogous odd-th power counts to A055653.
%C This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
%H T. D. Noe, <a href="/A085310/b085310.txt">Table of n, a(n) for n = 1..1000</a>
%H S. Li, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav86i2p113bwm">On the number of elements with maximal order in the multiplicative group modulo n</a>, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1
%p A085310 := proc(m)
%p {seq( modp(b^7,m),b=0..m-1) };
%p nops(%) ;
%p end proc:
%p seq(A085310(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017
%t a[n_] := Table[PowerMod[i, 7, n], {i, 0, n - 1}] // Union // Length;
%t Array[a, 100] (* _Jean-François Alcover_, Mar 24 2020 *)
%o (PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], my(k=f[i, 1]^f[i, 2]); #vecsort(vector(k, i, i^7%k), , 8)) \\ _Charles R Greathouse IV_, Sep 05 2013
%Y Cf. A000224[k=2], A046530[k=3], A052273[k=4], A052274[k=5], A052275[k=6], A085311[k=8], A085312[k=9], A085313[k=10], A085314[k=11], A228849[k=12], A055653.
%K nonn,mult
%O 1,2
%A _Labos Elemer_, Jun 27 2003
|
